Solve for $x$ and $y$ using elimination. ${3x-3y = -3}$ ${-2x+6y = 34}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ ${6x-6y = -6}$ $-2x+6y = 34$ Add the top and bottom equations together. $4x = 28$ $\dfrac{4x}{{4}} = \dfrac{28}{{4}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {3x-3y = -3}\thinspace$ to find $y$ ${3}{(7)}{ - 3y = -3}$ $21-3y = -3$ $21{-21} - 3y = -3{-21}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 7}$ into $\thinspace {-2x+6y = 34}\thinspace$ and get the same answer for $y$ : ${-2}{(7)}{ + 6y = 34}$ ${y = 8}$